Manufacturing processes for metallic and composite structures or materials may induce incompatibilities that result in residual stresses and/or distortion. The manufacturing processes may include forming operations such as extruding, forging, quenching, machining, laminate layup, curing, and the like, and post-forming operations such as shot peening, laser peening, ultrasonic impact forming (UIF), and the like. In a continuous elastic material, these incompatibilities are compensated for with a residual stress and distortion.
Typically, residual stresses may develop from a part of the incompatibilities that may be compensated for with a mechanical elastic strain field inside the material. The uncompensated part of the incompatibilities may produce distortion. In instances in which all of the incompatibilities may be compensated for by a compatible elastic strain field within the material, the residual stresses may develop without any distortion. Likewise, if no part of the incompatibilities may be balanced by a compatible strain field then the material may distort without the development of any residual stresses.
As used herein, the phrase initial stress in a material may be related to deformation, strain, or structural stress within the material of an article or structural element prior to relaxation via deformation of the article. Exemplary operations that may be performed on an article and thereby result in a deformation of the article may include manufacturing processes such as shot peening laser shock peening, or needle peening. Further, the phrase eigenstrain of a material may relate to deformation, strain, or structural stress within the material of an article that was imparted by external processing but remains after the external forces are released. Exemplary eigenstrain can include forces caused by shot peening, laser shock peening, or needle peening.
Within the context of residual stresses, initial stresses are defined as stresses obtained by direct conversion of incompatibilities caused by forming and/or manufacturing processes of a part. Residual stresses exist on a material in the absence of external loads and are a result of the relaxation of initial stresses for the purpose of achieving equilibrium (e.g., in the absence of external loads) within the material. In instances in which no plasticity is generated when the initial stresses relax, the relaxation may occur elastically. If a material is linear, the elastic relaxation may be given by the components of the initial stresses that do not satisfy equilibrium, in the absence of external loads, within the domain of the material. Reconstruction of initial stresses may require the estimation of residual stresses and the linear elastic relaxation of a coupon, part or component of a material.
Furthermore, initial stress may refer to forces per unit area related to differential equilibrium equations and an eigenstrain may be the spatial variations (differentials) of a displacement field. The relationship between initial stresses and eigenstrains may be denoted by typical properties of material law. For example, in the case of linear elasticity, the initial stress-eigenstrain relationship may be given by:σij=Cijklεkl or inversely by εkl=Cijkl−1σij where the coefficients of the Cijkl tensor are material properties characterized by the Lame constants. This relationship, well known and established in the fields of continuum mechanics or solid mechanics, is considered within the linear elastic range.
In general, calculation of either initial stresses or eigenstrains caused from a surface process from experimental data may require substantial measurements. Several surface and subsurface measurements are required in order to resolve spatial variations and to provide adequate information to extrapolate the linear elastic response of a material. Various methods may be utilized for the identification of initial stresses, and in some instances, these methods may require data derived from empirical observations in addition to calculated values. For typical methods, obtaining the residual stress measurements required to calculate the initial stress or eigenstrains may require a significant effort as the residual stresses act along the entire domain of the material. In particular, for surface processes, residual stresses are required to be measured past the penetration depth of the process and reflect substantial data points in order for observations of a linear elastic response to be feasible. In many instances, the linear elastic portion of the residual stress (e.g., the part of the material reacting to the plastic layer caused by the surface process) is affected by pre-existing residual stresses; therefore, the residual stresses on the linear elastic response of the material after the surface process may not be clearly distinguished unless additional residual stress measurements prior the surface process are generated in addition.